Caltech vs Stanford vs Princeton for mathematics?

Which uni out of the three would be the best to pursue an undergraduate degree in mathematics?

What are the major differences between these three universities? (especially for mathematics but also other things)

What are the pros/cons of each?

Did u get admitted into all 3 of them?

I don’t know anything first hand but a friend’s son was admitted to Princeton and Stanford last year and chose Princeton because of the math department but he was very specific about what he wanted to study and who he wanted to study with so not sure that he chose it because it was generally better, just that it had more of what he wanted.